Mozilla named a new chief executive this week to lead the non-profit Web organization as it tries to keep its Firefox browser relevant in the mobile age. The appointment has proved controversial in more ways than one.

Three Mozilla board members resigned over the choice of Brendan Eich, a Mozilla co-founder, as the new CEO. Gary Kovacs, a former Mozilla CEO who runs online security company AVG Technologies; John Lilly, another former Mozilla CEO now a partner at venture-capital firm Greylock Partners; and Ellen Siminoff, CEO of online education startup Shmoop, left the board last week.

The departures leave three people on the Mozilla board: co-founder Mitchell Baker; Reid Hoffman, co-founder of LinkedIn, and Katharina Borchert, chief executive of German news site Spiegel Online.

The three board members who resigned sought a CEO from outside Mozilla with experience in the mobile industry who could help expand the organization’s Firefox OS mobile-operating system and balance the skills of co-founders Eich and Baker, the people familiar with the situation said. They did not want to be identified because they are not authorized to speak publicly about the matter.

Mozilla spokesman Mike Manning confirmed the three remaining board members, but he declined to comment further on Friday. He did not immediately respond to a request to speak to Eich and Baker.

Firefox is the world’s second-most-popular Web browser on personal computers, with 18% market share, according to Net Applications, a web-analytics consulting firm. That trails Microsoft’s Internet Explorer, with 58% share, and just ahead of Google’s Chrome, with 17% share.

On mobile devices, however, Firefox ranks 13th, with less than 0.1% share, according to Net Applications. Apple’s Safari browser leads with 54% of the mobile-browser market, while Google’s Android and Chrome browsers have a combined 36% share.

Unlike Apple, Microsoft and Google, Mozilla is a non-profit organization focused on improving the web and keeping it open for users. Eich will have to balance this goal with the need to generate at least enough revenue to pay for the organization’s many projects.

The board departures are not the only source of early pressure on the new Mozilla CEO. Some employees of the organization are calling for Eich to step down because he donated $1,000 to the campaign in support of Proposition 8, a 2008 California ballot measure that banned same-sex marriage in the state.

“I do not support the Board’s appointment of @BrendanEich as CEO,” Kat Braybrooke, a curation and co-design lead at the organization, wrote on Twitter on Thursday:

“We expect and encourage Mozillians to speak up when they disagree with management decisions, and carefully weigh all input to ensure our actions are advancing the project’s mission,” he said in a statement.